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| # Copyright (c) Meta Platforms, Inc. and affiliates. | |
| # All rights reserved. | |
| # | |
| # This source code is licensed under the license found in the | |
| # LICENSE file in the root directory of this source tree. | |
| """ | |
| Functions for Noise Schedule, defines diffusion process, reverse process and data processor. | |
| """ | |
| from collections import namedtuple | |
| import random | |
| import typing as tp | |
| import julius | |
| import torch | |
| TrainingItem = namedtuple("TrainingItem", "noisy noise step") | |
| def betas_from_alpha_bar(alpha_bar): | |
| alphas = torch.cat([torch.Tensor([alpha_bar[0]]), alpha_bar[1:]/alpha_bar[:-1]]) | |
| return 1 - alphas | |
| class SampleProcessor(torch.nn.Module): | |
| def project_sample(self, x: torch.Tensor): | |
| """Project the original sample to the 'space' where the diffusion will happen.""" | |
| return x | |
| def return_sample(self, z: torch.Tensor): | |
| """Project back from diffusion space to the actual sample space.""" | |
| return z | |
| class MultiBandProcessor(SampleProcessor): | |
| """ | |
| MultiBand sample processor. The input audio is splitted across | |
| frequency bands evenly distributed in mel-scale. | |
| Each band will be rescaled to match the power distribution | |
| of Gaussian noise in that band, using online metrics | |
| computed on the first few samples. | |
| Args: | |
| n_bands (int): Number of mel-bands to split the signal over. | |
| sample_rate (int): Sample rate of the audio. | |
| num_samples (int): Number of samples to use to fit the rescaling | |
| for each band. The processor won't be stable | |
| until it has seen that many samples. | |
| power_std (float or list/tensor): The rescaling factor computed to match the | |
| power of Gaussian noise in each band is taken to | |
| that power, i.e. `1.` means full correction of the energy | |
| in each band, and values less than `1` means only partial | |
| correction. Can be used to balance the relative importance | |
| of low vs. high freq in typical audio signals. | |
| """ | |
| def __init__(self, n_bands: int = 8, sample_rate: float = 24_000, | |
| num_samples: int = 10_000, power_std: tp.Union[float, tp.List[float], torch.Tensor] = 1.): | |
| super().__init__() | |
| self.n_bands = n_bands | |
| self.split_bands = julius.SplitBands(sample_rate, n_bands=n_bands) | |
| self.num_samples = num_samples | |
| self.power_std = power_std | |
| if isinstance(power_std, list): | |
| assert len(power_std) == n_bands | |
| power_std = torch.tensor(power_std) | |
| self.register_buffer('counts', torch.zeros(1)) | |
| self.register_buffer('sum_x', torch.zeros(n_bands)) | |
| self.register_buffer('sum_x2', torch.zeros(n_bands)) | |
| self.register_buffer('sum_target_x2', torch.zeros(n_bands)) | |
| self.counts: torch.Tensor | |
| self.sum_x: torch.Tensor | |
| self.sum_x2: torch.Tensor | |
| self.sum_target_x2: torch.Tensor | |
| def mean(self): | |
| mean = self.sum_x / self.counts | |
| return mean | |
| def std(self): | |
| std = (self.sum_x2 / self.counts - self.mean**2).clamp(min=0).sqrt() | |
| return std | |
| def target_std(self): | |
| target_std = self.sum_target_x2 / self.counts | |
| return target_std | |
| def project_sample(self, x: torch.Tensor): | |
| assert x.dim() == 3 | |
| bands = self.split_bands(x) | |
| if self.counts.item() < self.num_samples: | |
| ref_bands = self.split_bands(torch.randn_like(x)) | |
| self.counts += len(x) | |
| self.sum_x += bands.mean(dim=(2, 3)).sum(dim=1) | |
| self.sum_x2 += bands.pow(2).mean(dim=(2, 3)).sum(dim=1) | |
| self.sum_target_x2 += ref_bands.pow(2).mean(dim=(2, 3)).sum(dim=1) | |
| rescale = (self.target_std / self.std.clamp(min=1e-12)) ** self.power_std # same output size | |
| bands = (bands - self.mean.view(-1, 1, 1, 1)) * rescale.view(-1, 1, 1, 1) | |
| return bands.sum(dim=0) | |
| def return_sample(self, x: torch.Tensor): | |
| assert x.dim() == 3 | |
| bands = self.split_bands(x) | |
| rescale = (self.std / self.target_std) ** self.power_std | |
| bands = bands * rescale.view(-1, 1, 1, 1) + self.mean.view(-1, 1, 1, 1) | |
| return bands.sum(dim=0) | |
| class NoiseSchedule: | |
| """Noise schedule for diffusion. | |
| Args: | |
| beta_t0 (float): Variance of the first diffusion step. | |
| beta_t1 (float): Variance of the last diffusion step. | |
| beta_exp (float): Power schedule exponent | |
| num_steps (int): Number of diffusion step. | |
| variance (str): choice of the sigma value for the denoising eq. Choices: "beta" or "beta_tilde" | |
| clip (float): clipping value for the denoising steps | |
| rescale (float): rescaling value to avoid vanishing signals unused by default (i.e 1) | |
| repartition (str): shape of the schedule only power schedule is supported | |
| sample_processor (SampleProcessor): Module that normalize data to match better the gaussian distribution | |
| noise_scale (float): Scaling factor for the noise | |
| """ | |
| def __init__(self, beta_t0: float = 1e-4, beta_t1: float = 0.02, num_steps: int = 1000, variance: str = 'beta', | |
| clip: float = 5., rescale: float = 1., device='cuda', beta_exp: float = 1, | |
| repartition: str = "power", alpha_sigmoid: dict = {}, n_bands: tp.Optional[int] = None, | |
| sample_processor: SampleProcessor = SampleProcessor(), noise_scale: float = 1.0, **kwargs): | |
| self.beta_t0 = beta_t0 | |
| self.beta_t1 = beta_t1 | |
| self.variance = variance | |
| self.num_steps = num_steps | |
| self.clip = clip | |
| self.sample_processor = sample_processor | |
| self.rescale = rescale | |
| self.n_bands = n_bands | |
| self.noise_scale = noise_scale | |
| assert n_bands is None | |
| if repartition == "power": | |
| self.betas = torch.linspace(beta_t0 ** (1 / beta_exp), beta_t1 ** (1 / beta_exp), num_steps, | |
| device=device, dtype=torch.float) ** beta_exp | |
| else: | |
| raise RuntimeError('Not implemented') | |
| self.rng = random.Random(1234) | |
| def get_beta(self, step: tp.Union[int, torch.Tensor]): | |
| if self.n_bands is None: | |
| return self.betas[step] | |
| else: | |
| return self.betas[:, step] # [n_bands, len(step)] | |
| def get_initial_noise(self, x: torch.Tensor): | |
| if self.n_bands is None: | |
| return torch.randn_like(x) | |
| return torch.randn((x.size(0), self.n_bands, x.size(2))) | |
| def get_alpha_bar(self, step: tp.Optional[tp.Union[int, torch.Tensor]] = None) -> torch.Tensor: | |
| """Return 'alpha_bar', either for a given step, or as a tensor with its value for each step.""" | |
| if step is None: | |
| return (1 - self.betas).cumprod(dim=-1) # works for simgle and multi bands | |
| if type(step) is int: | |
| return (1 - self.betas[:step + 1]).prod() | |
| else: | |
| return (1 - self.betas).cumprod(dim=0)[step].view(-1, 1, 1) | |
| def get_training_item(self, x: torch.Tensor, tensor_step: bool = False) -> TrainingItem: | |
| """Create a noisy data item for diffusion model training: | |
| Args: | |
| x (torch.Tensor): clean audio data torch.tensor(bs, 1, T) | |
| tensor_step (bool): If tensor_step = false, only one step t is sample, | |
| the whole batch is diffused to the same step and t is int. | |
| If tensor_step = true, t is a tensor of size (x.size(0),) | |
| every element of the batch is diffused to a independently sampled. | |
| """ | |
| step: tp.Union[int, torch.Tensor] | |
| if tensor_step: | |
| bs = x.size(0) | |
| step = torch.randint(0, self.num_steps, size=(bs,), device=x.device) | |
| else: | |
| step = self.rng.randrange(self.num_steps) | |
| alpha_bar = self.get_alpha_bar(step) # [batch_size, n_bands, 1] | |
| x = self.sample_processor.project_sample(x) | |
| noise = torch.randn_like(x) | |
| noisy = (alpha_bar.sqrt() / self.rescale) * x + (1 - alpha_bar).sqrt() * noise * self.noise_scale | |
| return TrainingItem(noisy, noise, step) | |
| def generate(self, model: torch.nn.Module, initial: tp.Optional[torch.Tensor] = None, | |
| condition: tp.Optional[torch.Tensor] = None, return_list: bool = False): | |
| """Full ddpm reverse process. | |
| Args: | |
| model (nn.Module): Diffusion model. | |
| initial (tensor): Initial Noise. | |
| condition (tensor): Input conditionning Tensor (e.g. encodec compressed representation). | |
| return_list (bool): Whether to return the whole process or only the sampled point. | |
| """ | |
| alpha_bar = self.get_alpha_bar(step=self.num_steps - 1) | |
| current = initial | |
| iterates = [initial] | |
| for step in range(self.num_steps)[::-1]: | |
| with torch.no_grad(): | |
| estimate = model(current, step, condition=condition).sample | |
| alpha = 1 - self.betas[step] | |
| previous = (current - (1 - alpha) / (1 - alpha_bar).sqrt() * estimate) / alpha.sqrt() | |
| previous_alpha_bar = self.get_alpha_bar(step=step - 1) | |
| if step == 0: | |
| sigma2 = 0 | |
| elif self.variance == 'beta': | |
| sigma2 = 1 - alpha | |
| elif self.variance == 'beta_tilde': | |
| sigma2 = (1 - previous_alpha_bar) / (1 - alpha_bar) * (1 - alpha) | |
| elif self.variance == 'none': | |
| sigma2 = 0 | |
| else: | |
| raise ValueError(f'Invalid variance type {self.variance}') | |
| if sigma2 > 0: | |
| previous += sigma2**0.5 * torch.randn_like(previous) * self.noise_scale | |
| if self.clip: | |
| previous = previous.clamp(-self.clip, self.clip) | |
| current = previous | |
| alpha_bar = previous_alpha_bar | |
| if step == 0: | |
| previous *= self.rescale | |
| if return_list: | |
| iterates.append(previous.cpu()) | |
| if return_list: | |
| return iterates | |
| else: | |
| return self.sample_processor.return_sample(previous) | |
| def generate_subsampled(self, model: torch.nn.Module, initial: torch.Tensor, step_list: tp.Optional[list] = None, | |
| condition: tp.Optional[torch.Tensor] = None, return_list: bool = False): | |
| """Reverse process that only goes through Markov chain states in step_list.""" | |
| if step_list is None: | |
| step_list = list(range(1000))[::-50] + [0] | |
| alpha_bar = self.get_alpha_bar(step=self.num_steps - 1) | |
| alpha_bars_subsampled = (1 - self.betas).cumprod(dim=0)[list(reversed(step_list))].cpu() | |
| betas_subsampled = betas_from_alpha_bar(alpha_bars_subsampled) | |
| current = initial * self.noise_scale | |
| iterates = [current] | |
| for idx, step in enumerate(step_list[:-1]): | |
| with torch.no_grad(): | |
| estimate = model(current, step, condition=condition).sample * self.noise_scale | |
| alpha = 1 - betas_subsampled[-1 - idx] | |
| previous = (current - (1 - alpha) / (1 - alpha_bar).sqrt() * estimate) / alpha.sqrt() | |
| previous_alpha_bar = self.get_alpha_bar(step_list[idx + 1]) | |
| if step == step_list[-2]: | |
| sigma2 = 0 | |
| previous_alpha_bar = torch.tensor(1.0) | |
| else: | |
| sigma2 = (1 - previous_alpha_bar) / (1 - alpha_bar) * (1 - alpha) | |
| if sigma2 > 0: | |
| previous += sigma2**0.5 * torch.randn_like(previous) * self.noise_scale | |
| if self.clip: | |
| previous = previous.clamp(-self.clip, self.clip) | |
| current = previous | |
| alpha_bar = previous_alpha_bar | |
| if step == 0: | |
| previous *= self.rescale | |
| if return_list: | |
| iterates.append(previous.cpu()) | |
| if return_list: | |
| return iterates | |
| else: | |
| return self.sample_processor.return_sample(previous) | |